Much of our technical work revolves around the result that \(\mathsf {D}:\mathbf {Set}\rightarrow \mathbf {Pos}\)  is dense, see [1]}, and that \(\mathsf {W}:\mathbf {BA}\rightarrow \mathbf {DL}\)  is codense, see Theorem REF . This in turn allows us to extend functors on \(\mathbf {Set}\)  to functors on \(\mathbf {Pos}\)  via left Kan extension and to extend functors on \(\mathbf {BA}\)  to functors on \(\mathbf {DL}\)  via right Kan extensions, as we will review now.
